Details

analyze585.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample2.0s (22.7%)

Symmetry

(sort re im)

Results

1.7s	8256×	body	128	valid
197.0ms	1044×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`rules-6_binary64`
568×	`rules-33_binary64`
520×	`cube-div_binary64`
414×	`rules-5-rev_binary64`
355×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	37	21
2	87	14
3	275	11
4	965	11
5	3981	11
6	4661	11
7	5451	11

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	31.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Status

Error

Program

▶

0.3b

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

31.3b

(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

series735.0ms (8.5%)

Counts

2 → 60

Calls

2 calls:

724.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
11.0ms	(hypot.f64 re im)

rewrite50.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
159×	`prod-diff_binary64`
138×	`log1p-udef_binary64`
77×	`add-sqr-sqrt_binary64`

Counts

2 → 60

Calls

2 calls:

48.0ms	(hypot.f64 re im)
48.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	174	15
2	2100	15
3	5162	15
0	0	0
1	0	0

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

586×	`rules-15-rev_binary64`
518×	`fma-neg_binary64`
361×	`rules-20_binary64`
284×	`rules-14-rev_binary64`
249×	`fma-udef_binary64`

Counts

120 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1694
1	415	1570
2	1694	1534
3	4907	1534
4	5101	1534

prune140.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	124	12	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	13	138

Error

0.0b

Counts

138 → 13

Alt Table

Status	Error	Program
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	16.1b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) 1)
	40.7b	(/.f64 (log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3)) (log.f64 base))
	0.7b	(cbrt.f64 (/.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3) (pow.f64 (log.f64 base) 3)))
	34.0b	(pow.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 2)
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) 3)
	14.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	1.3b	(*.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	14.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	1.3b	(/.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (cbrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	31.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))

Compiler

Compiled 2804 to 1512 computations (46.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series676.0ms (7.8%)

Counts

2 → 44

Calls

2 calls:

642.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms	(/.f64 1 (log.f64 base))

rewrite66.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

850×	`log1p-expm1-u_binary64`
850×	`expm1-log1p-u_binary64`
234×	`prod-diff_binary64`
104×	`egg-rr`
92×	`add-sqr-sqrt_binary64`

Counts

2 → 104

Calls

2 calls:

63.0ms	(/.f64 1 (log.f64 base))
63.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	217	17
2	2573	17
3	6101	17
0	0	0
1	0	0

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

457×	`rules-15-rev_binary64`
397×	`fma-neg_binary64`
364×	`rules-12-rev_binary64`
262×	`rules-20_binary64`
226×	`rules-14-rev_binary64`

Counts

148 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1292
1	293	1188
2	1201	1132
3	4882	1132
4	5026	1132

prune195.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	209	6	215
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	217	11	228

Error

0.0b

Counts

228 → 11

Alt Table

Status	Error	Program
	14.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	0.7b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	0.9b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	14.7b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 base)))
	0.9b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (log.f64 base) -2)) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (log.f64 (hypot.f64 re im))) (neg.f64 (.f64 0 (log.f64 (hypot.f64 re im))))) (fma.f64 0 (log.f64 (hypot.f64 re im)) (*.f64 0 (log.f64 (hypot.f64 re im)))))
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	31.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.2b	(+.f64 (fma.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (/.f64 1 (log.f64 base)) (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (neg.f64 (.f64 0 (log.f64 (hypot.f64 re im))))) (fma.f64 0 (log.f64 (hypot.f64 re im)) (*.f64 0 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 4709 to 2406 computations (48.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series1.2s (13.6%)

Counts

2 → 72

Calls

2 calls:

616.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
558.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite59.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

831×	`log1p-expm1-u_binary64`
831×	`expm1-log1p-u_binary64`
180×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Counts

2 → 61

Calls

2 calls:

58.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
58.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	215	22
2	2517	22
3	5860	22
0	0	0
1	0	0

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

341×	`rules-4_binary64`
296×	`rules-6_binary64`
261×	`fma-def_binary64`
237×	`rules-14-rev_binary64`
211×	`rules-13_binary64`

Counts

133 → 165

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	300	3474
1	1156	3193
2	5192	3193

prune181.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	226	11	237

Error

Counts

237 → 11

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.9b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	14.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	0.7b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.4b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1))
	31.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(+.f64 (fma.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (/.f64 1 (log.f64 base)) (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (neg.f64 (.f64 0 (log.f64 (hypot.f64 re im))))) (fma.f64 0 (log.f64 (hypot.f64 re im)) (*.f64 0 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
▶	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 6275 to 3582 computations (42.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(/.f64 1 (log.f64 (hypot.f64 re im)))
✓	0.3b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))

series594.0ms (6.9%)

Counts

2 → 60

Calls

2 calls:

552.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
42.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

rewrite71.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

756×	`fma-neg_binary64`
439×	`fma-def_binary64`
232×	`prod-diff_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Counts

2 → 125

Calls

2 calls:

68.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
68.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	239	20
2	2841	20
3	5034	20
0	0	0
1	0	0

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

248×	`fma-def_binary64`
229×	`rules-14-rev_binary64`
218×	`rules-6_binary64`
198×	`rules-13_binary64`
167×	`rules-21_binary64`

Counts

185 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	2808
1	1043	2676
2	4824	2642
3	4954	2642
4	4987	2642

prune252.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	310	11	321

Error

Counts

321 → 11

Alt Table

Status	Error	Program
	14.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 (hypot.f64 re im))))) (log.f64 base))
	0.7b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 1 (log.f64 base))))
	1.4b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) -1))
	31.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	0.9b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2))))
	0.6b	(cbrt.f64 (/.f64 (/.f64 1 (pow.f64 (log.f64 base) 3)) (/.f64 1 (pow.f64 (log.f64 (hypot.f64 re im)) 3))))
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(+.f64 (fma.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (/.f64 1 (log.f64 base)) (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) 2)) (neg.f64 (.f64 0 (log.f64 (hypot.f64 re im))))) (fma.f64 0 (log.f64 (hypot.f64 re im)) (*.f64 0 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) 3))
✓	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 7570 to 4326 computations (42.9% saved)

regimes1.2s (14.4%)

Accuracy

Total 0.3b remaining (90.5%)

Threshold costs 0.3b (90.5%)

Counts

218 → 1

Compiler

Compiled 19056 to 13421 computations (29.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	12	15
2	11	15

end165.0ms (1.9%)

Remove: (sort re im)
Compiler: Compiled 270 to 185 computations (31.5% saved)

Details

analyze585.0ms (6.8%)

sample2.0s (22.7%)

simplify64.0ms (0.7%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series735.0ms (8.5%)

rewrite50.0ms (0.6%)

simplify120.0ms (1.4%)

prune140.0ms (1.6%)

localize9.0ms (0.1%)

series676.0ms (7.8%)

rewrite66.0ms (0.8%)

simplify65.0ms (0.8%)

prune195.0ms (2.3%)

localize9.0ms (0.1%)

series1.2s (13.6%)

rewrite59.0ms (0.7%)

simplify72.0ms (0.8%)

prune181.0ms (2.1%)

localize9.0ms (0.1%)

series594.0ms (6.9%)

rewrite71.0ms (0.8%)

simplify109.0ms (1.3%)

prune252.0ms (2.9%)

regimes1.2s (14.4%)

simplify2.0ms (0%)

end165.0ms (1.9%)

Profiling